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Physics Unit 7: Electricity and circuits

Electric charges push and pull, and moving charges make current. Ohm's law and the rules for series and parallel circuits solve most circuit problems.

Covers: Charge and Coulomb's law, current, voltage, resistance, Ohm's law, series and parallel circuits, power

Study guide

Electric charge comes in positive and negative forms; like charges repel and opposite charges attract. Charge is measured in coulombs (C) and is conserved, and objects become charged by gaining or losing electrons through friction, conduction or induction. Conductors (metals) let charge move freely, while insulators don't. Coulomb's law gives the force between two charges: F = kq₁q₂/r², with k = 8.99 × 10⁹ N·m²/C². Like gravity, it follows an inverse-square law. An electric field describes the force per unit charge around a charge.

In a circuit, voltage (potential difference, in volts) is the energy per unit charge that pushes charges. Current is the rate of charge flow, I = Q/t, measured in amperes. Resistance opposes current, measured in ohms (Ω), and depends on the material, length and thickness of a conductor. Ohm's law ties them together: V = IR.

In a series circuit, components are connected end to end in a single path. The same current flows through each one, the voltages add up to the source voltage, and the total resistance is R = R₁ + R₂ + …. If one bulb breaks, the whole circuit stops.

In a parallel circuit, components are on separate branches. Each branch has the same voltage, the currents add up to the total current, and the total resistance comes from 1/R = 1/R₁ + 1/R₂ + …, which is always less than the smallest single resistor. Homes are wired in parallel.

Electric power is P = IV, which can also be written I²R or V²/R. Energy used equals power times time, and utilities bill in kilowatt-hours.

A wire's resistance is R = ρL/A, where ρ is the material's resistivity, L is its length and A is its cross-sectional area. Doubling the length doubles the resistance, and doubling the area halves it. Resistance also usually increases with temperature. Charge comes in whole-number multiples of the elementary charge, e = 1.60 × 10⁻¹⁹ C. An electron has −e, a proton +e and an alpha particle +2e. An electron-volt (eV) is the energy one elementary charge gains across 1 V, or 1.60 × 10⁻¹⁹ J.

Electric field lines point away from positive charges and toward negative ones. Between two oppositely charged parallel plates, the field is uniform and points from the positive plate to the negative plate. The force on a charge is F = qE: along the field for a positive charge and opposite to it for a negative charge. A current-carrying wire is surrounded by a magnetic field that circles the wire; point your right thumb along the current, and your fingers curl in the field's direction. Magnetic field lines run from a magnet's north pole to its south pole outside the magnet, and a compass needle lines up with the field.

An ammeter measures current and goes in series with the component. It has very low resistance. A voltmeter measures potential difference and goes in parallel across the component. It has very high resistance.

Key ideas

• Like charges repel; opposite charges attract.
• Current is charge flow (amps); voltage is energy per charge (volts); resistance opposes current (ohms).
• Ohm's law: V = IR.
• Series: one path, same current, resistances add.
• Parallel: multiple paths, same voltage, total resistance is less than the smallest branch.

Formulas and rules

Common mistakes

• Adding parallel resistances directly.
• Thinking current is used up by a resistor. Current is the same all along a series loop.

Words to know

Ohm's law

V = IR

Electric power

P = IV

Series resistance

R = R₁ + R₂ + …

Parallel circuit

Branches share the same voltage; currents add.

Ohm (Ω)

The unit of resistance.

Parallel resistance

1/R = 1/R₁ + 1/R₂ + …

Electric charge

Positive or negative; like charges repel, opposites attract.

Coulomb (C)

The unit of charge.

Conductor vs. insulator

Charges move freely in conductors, not in insulators.

Coulomb's law

F = kq₁q₂/r²

Electric field

Force per unit charge around a charge.

Voltage

Energy per unit charge (volts).

Current

Rate of charge flow, I = Q/t (amperes).

Resistance

Opposition to current (ohms).

Series circuit

One path; same current through every component.

Kilowatt-hour

A unit of energy: 1 kW for 1 hour.

Sample practice questions

21 more questions like these, from level 1 to 5, are in the practice set.